Why does apt-get complain "no space left on device" when I have 3GB free?

Question

One of my systems (16.04) has disk space left:

root@ip-172:/# df -k
Filesystem     1K-blocks    Used Available Use% Mounted on
udev              284388       0    284388   0% /dev
tmpfs              60120    6596     53524  11% /run
/dev/xvda1       8125880 4530864   3159204  59% /
tmpfs             300596       0    300596   0% /dev/shm
tmpfs               5120       0      5120   0% /run/lock
tmpfs             300596       0    300596   0% /sys/fs/cgroup
tmpfs                100       0       100   0% /run/lxcfs/controllers
tmpfs              60120       0     60120   0% /run/user/1000

When starting apt-get, I get errors due to missing disk space:

root@ip-172:~# apt-get -f install
Reading package lists... Done
Building dependency tree
Reading state information... Done
Correcting dependencies... Done
The following packages were automatically installed and are no longer required:
  linux-headers-4.4.0-24 linux-headers-4.4.0-24-generic linux-headers-4.4.0-28 linux-headers-4.4.0-28-generic
  linux-headers-4.4.0-31 linux-headers-4.4.0-31-generic linux-headers-4.4.0-34 linux-headers-4.4.0-34-generic
  (...)
Suggested packages:
  fdutils linux-doc-4.4.0 | linux-source-4.4.0 linux-tools
The following NEW packages will be installed:
  linux-headers-4.4.0-66 linux-headers-4.4.0-93 linux-headers-4.4.0-93-generic linux-image-4.4.0-93-generic
0 upgraded, 4 newly installed, 0 to remove and 174 not upgraded.
5 not fully installed or removed.
Need to get 0 B/42.7 MB of archives.
After this operation, 215 MB of additional disk space will be used.
Do you want to continue? [Y/n]
(Reading database ... 515059 files and directories currently installed.)
Preparing to unpack .../linux-headers-4.4.0-66_4.4.0-66.87_all.deb ...
Unpacking linux-headers-4.4.0-66 (4.4.0-66.87) ...
dpkg: error processing archive /var/cache/apt/archives/linux-headers-4.4.0-66_4.4.0-66.87_all.deb (--unpack):
 unable to create '/usr/src/linux-headers-4.4.0-66/sound/usb/hiface/Makefile.dpkg-new' (while processing './usr/src/linux-headers-4.4.0-66/sound/usb/hiface/Makefile'): No space left on device
No apport report written because the error message indicates a disk full error
                                                                              dpkg-deb: error: subprocess paste was killed by signal (Broken pipe)
Preparing to unpack .../linux-headers-4.4.0-93_4.4.0-93.116_all.deb ...
Unpacking linux-headers-4.4.0-93 (4.4.0-93.116) ...
dpkg: error processing archive /var/cache/apt/archives/linux-headers-4.4.0-93_4.4.0-93.116_all.deb (--unpack):
 unable to create '/usr/src/linux-headers-4.4.0-93/arch/x86/include/asm/pvclock.h.dpkg-new' (while processing './usr/src/linux-headers-4.4.0-93/arch/x86/include/asm/pvclock.h'): No space left on device
No apport report written because the error message indicates a disk full error
                                                                              dpkg-deb: error: subprocess paste was killed by signal (Broken pipe)
Preparing to unpack .../linux-headers-4.4.0-93-generic_4.4.0-93.116_amd64.deb ...
Unpacking linux-headers-4.4.0-93-generic (4.4.0-93.116) ...
dpkg: error processing archive /var/cache/apt/archives/linux-headers-4.4.0-93-generic_4.4.0-93.116_amd64.deb (--unpack):
 unable to create '/usr/src/linux-headers-4.4.0-93-generic/include/config/x86/cmpxchg64.h.dpkg-new' (while processing './usr/src/linux-headers-4.4.0-93-generic/include/config/x86/cmpxchg64.h'): No space left on device
No apport report written because the error message indicates a disk full error
                                                                              dpkg-deb: error: subprocess paste was killed by signal (Broken pipe)
Preparing to unpack .../linux-image-4.4.0-93-generic_4.4.0-93.116_amd64.deb ...
Done.
(...)

I still have 3GB left on / so I do not understand which disk exact space is missing?

Just in case I forced an fsck on reboot (and rebooted) but the issue is still there.